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Density behind oblique shock for given upstream density and normal upstream Mach number Calculator

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✖Density ahead of shock is the density of the fluid in the upstream direction of shock.ⓘ Density ahead of shock [ρ 1]
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✖The Specific Heat Ratio Dynamic is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.ⓘ Specific Heat Ratio Dynamic [κ]
+10%
-10%
✖Component of upstream mach normal to oblique shock is that component of upstream Mach number which is normal to oblique shockwave.ⓘ Component of upstream mach normal to oblique shock [Mn1]
+10%
-10%
✖Density behind shock is the density of the fluid in the upstream direction of shock.ⓘ Density behind oblique shock for given upstream density and normal upstream Mach number [ρ 2]
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Density behind oblique shock for given upstream density and normal upstream Mach number

Formula
`"ρ "_{"2"} = "ρ "_{"1"}*(("κ"+1)*("M"_{"n1"}^2)/(2+(("κ"-1)*("M"_{"n1"}^2))))`

Example
`"3.752261kg/m³"="1.4kg/m³"*(("1.392758"+1)*(("2")^2)/(2+(("1.392758"-1)*(("2")^2))))`

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Density behind oblique shock for given upstream density and normal upstream Mach number Solution

STEP 0: Pre-Calculation Summary
Formula Used
Density behind Shock = Density ahead of shock*((Specific Heat Ratio Dynamic+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific Heat Ratio Dynamic-1)*(Component of upstream mach normal to oblique shock^2))))
ρ 2 = ρ 1*((κ+1)*(Mn1^2)/(2+((κ-1)*(Mn1^2))))
This formula uses 4 Variables
Variables Used
Density behind Shock - (Measured in Kilogram per Cubic Meter) - Density behind shock is the density of the fluid in the upstream direction of shock.
Density ahead of shock - (Measured in Kilogram per Cubic Meter) - Density ahead of shock is the density of the fluid in the upstream direction of shock.
Specific Heat Ratio Dynamic - The Specific Heat Ratio Dynamic is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.
Component of upstream mach normal to oblique shock - Component of upstream mach normal to oblique shock is that component of upstream Mach number which is normal to oblique shockwave.
STEP 1: Convert Input(s) to Base Unit
Density ahead of shock: 1.4 Kilogram per Cubic Meter --> 1.4 Kilogram per Cubic Meter No Conversion Required
Specific Heat Ratio Dynamic: 1.392758 --> No Conversion Required
Component of upstream mach normal to oblique shock: 2 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ρ 2 = ρ 1*((κ+1)*(Mn1^2)/(2+((κ-1)*(Mn1^2)))) --> 1.4*((1.392758+1)*(2^2)/(2+((1.392758-1)*(2^2))))
Evaluating ... ...
ρ 2 = 3.7522611950831
STEP 3: Convert Result to Output's Unit
3.7522611950831 Kilogram per Cubic Meter --> No Conversion Required
FINAL ANSWER
3.7522611950831 Kilogram per Cubic Meter <-- Density behind Shock
(Calculation completed in 00.015 seconds)
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Created by Shikha Maurya
Indian Institute of Technology (IIT), Bombay
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PSG College of Technology (PSGCT), Coimbatore
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19 Oblique Shock and Expansion Waves Calculators

Temperature behind oblique shock for given upstream temperature and normal upstream Mach number
Go Temperature behind Shock = Temperature ahead of Shock*((1+((2*Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic+1))*((Component of upstream mach normal to oblique shock^2)-1))/((Specific Heat Ratio Dynamic+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific Heat Ratio Dynamic-1)*(Component of upstream mach normal to oblique shock^2)))))
Prandtl Meyer function at upstream Mach number
Go Prandtl Meyer Function at upstream Mach no. = sqrt((Specific Heat Ratio Dynamic+1)/(Specific Heat Ratio Dynamic-1))*atan(sqrt(((Specific Heat Ratio Dynamic-1)*((Mach Number ahead of shock^2)-1))/(Specific Heat Ratio Dynamic+1)))-atan(sqrt(((Mach Number ahead of shock^2)-1)))
Prandtl Meyer function
Go Prandtl Meyer Function = sqrt((Specific Heat Ratio Dynamic+1)/(Specific Heat Ratio Dynamic-1))*atan(sqrt(((Specific Heat Ratio Dynamic-1)*((Mach Number^2)-1))/(Specific Heat Ratio Dynamic+1)))-atan(sqrt(((Mach Number^2)-1)))
Temperature Ratio across Oblique Shock
Go Temperature Ratio across Shock = (1+((2*Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic+1))*((Component of upstream mach normal to oblique shock^2)-1))/((Specific Heat Ratio Dynamic+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific Heat Ratio Dynamic-1)*(Component of upstream mach normal to oblique shock^2))))
Flow deflection angle
Go Flow Deflection angle = atan((2*cot(Oblique shock angle)*(((Mach Number ahead of shock*sin(Oblique shock angle))^2)-1))/(((Mach Number ahead of shock^2)*(Specific Heat Ratio Dynamic+cos(2*Oblique shock angle)))+2))
Pressure behind expansion fan
Go Pressure behind expansion fan = Pressure ahead Expansion Fan*((1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach Number ahead Expansion Fan^2))/(1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach Number behind Expansion Fan^2)))^((Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic-1))
Component of downstream Mach number normal to oblique shock for given normal upstream Mach number
Go Downstream Mach Normal to Oblique Shock = sqrt((1+0.5*((Specific Heat Ratio Dynamic-1)*Component of upstream mach normal to oblique shock^2))/(Specific Heat Ratio Dynamic*Component of upstream mach normal to oblique shock^2-0.5*(Specific Heat Ratio Dynamic-1)))
Pressure Ratio across Expansion Fan
Go Pressure Ratio across Expansion Fan = ((1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach Number ahead Expansion Fan^2))/(1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach Number behind Expansion Fan^2)))^((Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic-1))
Density behind oblique shock for given upstream density and normal upstream Mach number
Go Density behind Shock = Density ahead of shock*((Specific Heat Ratio Dynamic+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific Heat Ratio Dynamic-1)*(Component of upstream mach normal to oblique shock^2))))
Temperature behind expansion fan
Go Temperature behind Expansion Fan = Temperature ahead Expansion Fan*((1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach Number ahead Expansion Fan^2))/(1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach Number behind Expansion Fan^2)))
Density Ratio across Oblique Shock
Go Density Ratio across Shock = (Specific Heat Ratio Dynamic+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific Heat Ratio Dynamic-1)*(Component of upstream mach normal to oblique shock^2)))
Temperature Ratio across Expansion Fan
Go Temperature Ratio across Expansion Fan = (1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach Number ahead Expansion Fan^2))/(1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach Number behind Expansion Fan^2))
Pressure behind oblique shock for given upstream pressure and normal upstream Mach number
Go Static pressure behind shock = Static pressure ahead of shock*(1+((2*Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic+1))*((Component of upstream mach normal to oblique shock^2)-1))
Pressure Ratio across Oblique shock
Go Pressure Ratio across Shock = 1+((2*Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic+1))*((Component of upstream mach normal to oblique shock^2)-1)
Component of Downstream Mach normal to oblique shock
Go Downstream Mach Normal to Oblique Shock = Mach Number behind shock*sin(Oblique shock angle-Flow Deflection angle)
Component of Upstream Mach normal to oblique shock
Go Component of upstream mach normal to oblique shock = Mach Number ahead of shock*sin(Oblique shock angle)
Flow Deflection Angle using Prandtl Meyer function
Go Flow Deflection angle = Prandtl Meyer Function at downstream Mach no.-Prandtl Meyer Function at upstream Mach no.
Rearward Mach Angle of Expansion Fan
Go Rearward Mach Angle = arsin(1/Mach Number behind Expansion Fan)
Forward Mach angle of expansion fan
Go Forward Mach Angle = arsin(1/Mach Number ahead Expansion Fan)

Density behind oblique shock for given upstream density and normal upstream Mach number Formula

Density behind Shock = Density ahead of shock*((Specific Heat Ratio Dynamic+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific Heat Ratio Dynamic-1)*(Component of upstream mach normal to oblique shock^2))))
ρ 2 = ρ 1*((κ+1)*(Mn1^2)/(2+((κ-1)*(Mn1^2))))

Which parameters govern the changes of flow properties across oblique shock?

Oblique shock wave properties in a calorically perfect gas depend only on the normal component of upstream Mach no and which in turn is a function of upstream Mach no. and wave angle. In contrast, the changes in flow properties across normal shock depend on upstream Mach no only.

How to Calculate Density behind oblique shock for given upstream density and normal upstream Mach number?

Density behind oblique shock for given upstream density and normal upstream Mach number calculator uses Density behind Shock = Density ahead of shock*((Specific Heat Ratio Dynamic+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific Heat Ratio Dynamic-1)*(Component of upstream mach normal to oblique shock^2)))) to calculate the Density behind Shock, The Density behind oblique shock for given upstream density and normal upstream Mach number formula is obtained by multiplying density ratio across the oblique shock to the density ahead of the oblique shock. Density behind Shock is denoted by ρ 2 symbol.

How to calculate Density behind oblique shock for given upstream density and normal upstream Mach number using this online calculator? To use this online calculator for Density behind oblique shock for given upstream density and normal upstream Mach number, enter Density ahead of shock (ρ 1), Specific Heat Ratio Dynamic (κ) & Component of upstream mach normal to oblique shock (Mn1) and hit the calculate button. Here is how the Density behind oblique shock for given upstream density and normal upstream Mach number calculation can be explained with given input values -> 3.752261 = 1.4*((1.392758+1)*(2^2)/(2+((1.392758-1)*(2^2)))).

FAQ

What is Density behind oblique shock for given upstream density and normal upstream Mach number?
The Density behind oblique shock for given upstream density and normal upstream Mach number formula is obtained by multiplying density ratio across the oblique shock to the density ahead of the oblique shock and is represented as ρ 2 = ρ 1*((κ+1)*(Mn1^2)/(2+((κ-1)*(Mn1^2)))) or Density behind Shock = Density ahead of shock*((Specific Heat Ratio Dynamic+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific Heat Ratio Dynamic-1)*(Component of upstream mach normal to oblique shock^2)))). Density ahead of shock is the density of the fluid in the upstream direction of shock, The Specific Heat Ratio Dynamic is the ratio of the heat capacity at constant pressure to heat capacity at constant volume & Component of upstream mach normal to oblique shock is that component of upstream Mach number which is normal to oblique shockwave.
How to calculate Density behind oblique shock for given upstream density and normal upstream Mach number?
The Density behind oblique shock for given upstream density and normal upstream Mach number formula is obtained by multiplying density ratio across the oblique shock to the density ahead of the oblique shock is calculated using Density behind Shock = Density ahead of shock*((Specific Heat Ratio Dynamic+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific Heat Ratio Dynamic-1)*(Component of upstream mach normal to oblique shock^2)))). To calculate Density behind oblique shock for given upstream density and normal upstream Mach number, you need Density ahead of shock (ρ 1), Specific Heat Ratio Dynamic (κ) & Component of upstream mach normal to oblique shock (Mn1). With our tool, you need to enter the respective value for Density ahead of shock, Specific Heat Ratio Dynamic & Component of upstream mach normal to oblique shock and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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